Wavefront coding interference contrast imaging systems

ABSTRACT

Contrast Imaging apparatus and methods with Wavefront Coding aspheric optics and post processing increase depth of field and reduce misfocus effects in imaging Phase Objects. The general Interference Contrast imaging system is modified with a special purpose optical element and image processing of the detected image to form the final image. The Wavefront Coding optical element can be fabricated as a separate component, can be constructed as an integral component of the imaging objective, tube lens, beam splitter, polarizer or any combination of such.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This patent application is a continuation of commonly-owned andcopending U.S. patent application Ser. No. 09/875,766, filed on Jun. 6,2001, and which is hereby incorporated herein by reference.

[0002] This patent application is also a continuation-in-part ofcommonly-owned and copending U.S. patent application Ser. No.09/070,969, filed on May 1, 1998; which is a continuation-in-part ofU.S. patent application Ser. No. 08/823,894 filed Mar. 17, 1997, nowU.S. Pat. No. 5,748,371; which is a continuation of U.S. patentapplication Ser. No. 08/384,257, filed Feb. 3, 1995, now abandoned, allof which are incorporated herein by reference.

[0003] This patent application also relates to commonly-owned andcopending U.S. patent application Ser. No. 09/766,325, filed Jan. 19,2001, which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

[0004] 1. Field of the Invention

[0005] This invention relates to apparatus and methods for usingWavefront Coding to improve contrast imaging of objects which aretransparent, reflective or vary in thickness or index of refraction.

[0006] 2. Description of the Prior Art

[0007] Most imaging systems generate image contrast through variationsin reflectance or absorption of the object being viewed. Objects thatare transparent or reflective but have variations in index of refractionor thickness can be very difficult to image. These types of transparentor reflective objects can be considered “Phase Objects”. Varioustechniques have been developed to produce high contrast images fromessentially transparent objects that have only variations in thicknessor index of refraction. These techniques generally modify both theillumination optics and the imaging optics and are different modes ofwhat can be called “Contrast Imaging”.

[0008] There are a number of different Contrast Imaging techniques thathave been developed over the years to image Phase Objects. Thesetechniques can be grouped into three classes that are dependent on thetype of modification made to the back focal plane of the imagingobjective and the type of illumination method used. The simplestContrast Imaging techniques modify the back focal plane of the imagingobjective with an intensity or amplitude mask. Other techniques modifythe back focal plane of the objective with phase masks. Still moretechniques, require the use of polarized illumination andpolarization-sensitive beam splitters and shearing devices.

[0009] Contrast Imaging techniques that require polarizers, beamsplitters and beam shearing to image optical phase gradients, we call“Interference Contrast” techniques. These techniques includeconventional Differential Interference Contrast (Smith, L. W.,Microscopic interferometry, Research (London), 8:385-395, 1955),improvements using Nomarski prisms (Allen, R. D., David, G. B, andNomarski, G, The Zeiss-Nomarski differential interference equipment fortransmitted light microscopy, Z. Wiss. Mikrosk. 69:193-221, 1969), theDyson interference microscope (Born and Wolf, Principals of Optics,Macmillan, 1964), the Jamin-Lebedeff interferometer microscopes asdescribed by Spencer in 1982 (“Fundamentals of Light Microscopy”,Cambridge University Press, London), and Mach-Zehnder type interferencemicroscopes (“Video Microscopy”, Inoue and Spring, Plenum Press, NewYork, 1997). Other related techniques include those that use reducedcost beam splitters and polarizers (U.S. Pat. No. 4,964,707), systemsthat employ contrast enhancement of the detected images (U.S. Pat. No.5,572,359), systems that vary the microscope phase settings and combinea multiplicity of images (U.S. Pat. No. 5,969,855), and systems havingvariable amounts of beam shearing (U.S. Pat. No. 6,128,127).

[0010]FIG. 1 (Prior Art) is a block diagram 100, which shows generallyhow Interference Contrast Imaging techniques are implemented. This blockdiagram shows imaging of a Phase Object 110 through transmission, butthose skilled in the art will appreciate that the elements could just assimply have been arranged to show imaging through reflection.

[0011] Illumination source 102 and polarizer 104 act to form linearlypolarized light. Beam splitter 106 divides the linearly polarized lightinto two linearly polarized beams that are orthogonally polarized. Suchorthogonal beams can be laterally displaced or sheared relative to eachother. Illumination optics 108 act to produce focussed light upon PhaseObject 110. A Phase Object is defined here as an object that istransparent or reflective but has variations in thickness and/or indexof refraction, and thus can be difficult to image because the majorityof the image contrast typically is derived from variations in thereflectance or absorbtion of the object.

[0012] Objective lens 112 and tube lens 118 act to produce an image upondetector 120. Beam splitter 114 acts to remove the lateral shear betweenthe two orthogonally polarized beams formed by beam splitter 106. Beamsplitter 114 is also generally adjustable. By adjusting this beamsplitter a phase difference between the two orthogonal beams can berealized. Analyzer 116 acts to combine the orthogonal beams byconverting them to the same linear polarization. Detector 122 can befilm, a CCD detector array, a CMOS detector, etc. Traditional imaging,such as bright field imaging, would result if polarizer and analyzer 104and 116 and beam splitters 106 and 114 were not used.

[0013]FIG. 2 (Prior Art) shows a description of the ray path andpolarizations through the length of the Interference Contrast imagingsystem of FIG. 1. The lower diagram of FIG. 2 describes the ray pathwhile the upper diagram describes the polarizations. The illuminationlight is linearly polarized after polarizer 204. This linearpolarization is described as a vertical arrow in the upper diagramdirectly above polarizer 204. At beam splitter 206 the single beam oflight becomes two orthogonally polarized beams of light that arespatially displaced or sheared with respect to each other. This isindicated by the two paths (solid and dotted) in both diagrams. Noticethat the two polarization states of the two paths in the top diagram areorthogonally rotated with respect to each other. Beam splitter 214spatially combines the two polarizations with a possible phase offset orbias. This phase bias is given by the parameter Δ in the upper plot. Bylaterally adjusting the second beam splitter 214 the value of the phasebias Δ can be changed. A Nomarski type prism is described by the raypath diagram, although a Wollaston type prism could have been used aswell. Analyzer 216 acts to convert the orthogonal component beams tolinearly polarized light. The angle between the polarizer 204 andanalyzer 216 can typically be varied in order to adjust the backgroundintensity. Image plane 218 acts to display or record a time averageintensity of the linearly polarized light, the sheared componentpossibly containing a phase shift. This image plane can be an opticalviewing device or a digital detector such as CCD, CMOS, etc.

[0014] The interactions of the polarizers, beam splitters, and PhaseObjects of the Interference Contrast imaging systems have been studiedin great detail. For additional background information see “Confocaldifferential interference contrast (DIC) microscopy: including atheoretical analysis of conventional and confocal DIC imaging”, Cogswelland Sheppard, Journal of Microscopy, Vol 165, Pt 1, January 1992, pp81-101.

[0015] In order to understand the relationship between the object,image, and phase shift Δ consider an arbitrary spatially constant objectthat can be mathematically described as:

[0016] Obj=a exp (jθ), where j={square root}{square root over (−1)}

[0017] where “a” is the amplitude and θ is the object phase. If the twocomponent beams of the system of FIG. 2 have equal amplitude, and if thecomponent beams are subtracted with relative phases +−662 then justafter analyzer 216 the resulting image amplitude is given by:

[0018] amp=a exp(j[θ−Δ2])−a exp(j[θ+Δ2])=2 j a exp(jθ) sin(Δ/2)

[0019] The image intensity is the square of the image amplitude. Theintensity of this signal is then given by:

[0020] int₀=4a² sin(Δ/2)².

[0021] The image intensity is independent of the object phase θ. Thephase difference or bias between the two orthogonal beams is given by Δand is adjusted by lateral movement of the beam splitter, be it aWollaston or a Nomarski type. If instead of a spatially constant object,consider an object whose phase varies by Δφ between two laterallysheared beams. This object phase variation is equivalent to a change inthe value of the component beam phases of Δ. If the component beamphases Δ is equal to zero (no relative phase shift) then the resultingimage intensity can be shown to have increases in intensity for bothpositive and negative variations of object phase. If the component beambias is increased so that the total phase variation is always positive,the change in image intensity then increases monotonically throughoutthe range Δφ. The actual value of the change in image intensity withobject phase change Δφ can be shown to be:

[0022] Int₁=4a² Δφsin(Δ).

[0023] Interference Contrast imaging the phase bias Δ determines therelative strengths with which the phase and amplitude information of theobject will be displayed in the image. If the object has amplitudevariations these will be imaged according to int₀ above. At a phase biasof zero (or multiple of 2 pi ) the image will contain a maximum of phaseinformation but a minimum of amplitude information. At a phase bias ofpi the opposite is true, with the image giving a maximum of amplitudeinformation of the object and a minimum of phase information. Forintermediate values of phase bias both phase and amplitude are imagedand the typical Interference Contrast bias relief image is produced, asis well known.

[0024] Variation of the phase bias can be shown to affect the parametersof image contrast, linearity, and signal-to-noise ratio (SNR) as well.The ratio of contrast from phase and amplitude in Interference Contrastimaging can be shown to be given by:

[0025] [contrast due to phase/contrast due to amplitude]=2 cot(Δ/2)

[0026] The overall contrast in the Interference Contrast image is theratio of the signal strength to the background and can be shown to begiven by:

[0027] overall contrast=2Δφcot(Δ2).

[0028] The linearity between the image intensity and phase gradients inthe object can be described by:

[0029] L=[(1+sin(Δ))^((2/3))]/[2cos(Δ)].

[0030] The signal-to-noise ratio (SNR), ignoring all sources of noiseexcept shot noise on the background, can be shown to be given by

[0031] SNR=4a cos(Δ/2).

[0032] In Interference Contrast imaging systems the condenser aperturecan be opened to improve resolution, although in practice, to maintaincontrast, the condenser aperture is usually not increased to fullillumination. Imaging is typically then partially coherent. Descriptionof the imaging characteristics for Interference Contrast imagingtherefore needs to be expressed in terms of a partially coherenttransfer function. The partially coherent transfer function (ortransmission cross-coefficient), given as C(m,n;p,q), describes thestrength of image contributions from pairs of spatial frequenciescomponents m; p in the x direction and n; q in the y direction (Born andWolf, Principals of Optics, Macmillan, 1975, p. 526). The intensity ofthe image in terms of the partially coherent transfer function image canbe written as:

[0033] I(x,y)=ƒƒƒƒT(m,n)T(p,g)*C(m,n;p,q)

[0034] exp(2pi j [(m−p)x+(n−q)y]) dm dn dp dq

[0035] where the limits of integration are + infinity to − infinity. Theterm T(m,n) is the spatial frequency content of the object amplitudetransmittance t(x,y):

[0036] T(m,n)=ƒƒ(x,y) exp(2pi j [mx+ny]) dx dy where again the limits ofintegration are +infinity to −infinity. ( )* denotes complex conjugate.When the condenser aperture is maximally opened and matched to the backaperture or exit pupil of the objective lens, the partially coherenttransfer function reduces to (Intro. to Fourier Optics, Goodman, 1968,pg. 120):

[0037] C(m, n; p, q)=δ(m−n)δ(p−q) [acosρ)−ρsqrt{(1−ρ² )}]

[0038] where ρ=sqrt(m²+p2) and δ(x)=1 if x=0, δ(x)=0 otherwise.

[0039] The effective transfer function for the Interference Contrastimaging system can be shown to be given as:

[0040] C(m,n;p,q)_(eff)=2 C(m,n;p,q) {cos[2 pi(m−n)Λ]−cos(Δ) cos([2pi(m+n) Λ]- sin(Δ)sin[2 pi (m+p)Λ]}

[0041] where Λis equal to the lateral shear of the beam splitters andC(m,n;p,q) is the partially coherent transfer function of the systemwithout Interference Contrast modifications.

[0042] Interference Contrast imaging is one of the most complex forms ofimaging in terms of analysis and design. These systems are also widelyused and studied. But, there is still a need to improve InterferenceContrast Imaging of Phase Objects by increasing the depth of field forimaging thick objects, as well as for controlling focus-relatedaberrations in order to produce less expensive imaging systems than iscurrently possible.

SUMMARY OF THE INVENTION

[0043] An object of the present invention is to improve Contrast Imagingof Phase Objects by increasing depth of field and controllingfocus-related aberrations. This is accomplished by using ContrastImaging apparatus and methods with Wavefront Coding aspheric optics andpost processing to increase depth of field and reduce misfocus effects.The general Interference Contrast imaging system is modified with aspecial purpose optical element and image processing of the detectedimage to form the final image. Unlike the conventional InterferenceContrast imaging system, the final Wavefront Coding InterferenceContrast image is not directly available at the image plane. Postprocessing of the detected image is required. The Wavefront Codingoptical element can be fabricated as a separate component, can beconstructed as an integral component of the imaging objective, tubelens, beam splifter, polarizer or any combination of such.

[0044] Apparatus for increasing depth of field and controlling focusrelated aberrations in an Interference Contrast Imaging system having anillumination source, optical elements for splitting light polarizations,and illumination optics placed before a Phase Object to be imaged, andelements for recombining light polarizations and objective optics afterthe Phase Object to form an image at a detector, includes an opticalWavefront Coding mask having an aperture and placed between the PhaseObject and the detector, the coding mask being constructed and arrangedto alter the optical transfer function of the Interference ContrastImaging system in such a way that the altered optical transfer functionis substantially insensitive to the distance between the Phase Objectand the objective optics over a greater range of object distances thanwas provided by the unaltered optical transfer function, wherein thecoding mask affects the alteration to the optical transfer functionsubstantially by affecting the phase of light transmitted by the mask.The system further includes a post processing element for processing theimage captured by the detector by reversing the alteration of theoptical transfer function accomplished by the coding mask.

[0045] The detector might be a charge coupled device (CCD).

[0046] The phase of light transmitted by the coding mask is preferablyrelatively flat near the center of the aperture with increasing anddecreasing phase near respective ends of the aperture.

[0047] As an alternative, the phase of light transmitted by the codingmask could substantially follow a cubic function.

[0048] In one embodiment, the phase of light transmitted by the codingmask substantially follows a function of the form:

[0049] Phase (x,y)=12 [x³+y³]

[0050] where |x|≦1, |y|≦1.

[0051] In another embodiment the phase of light transmitted by thecoding mask substantially follows a rectangularly separable sum ofpowers function of the form:

[0052] phase(x,y)=Σ[a_(i) sign(x) |x| ^(b) ^(_(i)) +c_(i) sign(y)|Y|^(d) ^(_(i)) ]

[0053] where the sum is over the index i,

[0054] sign(x)=−1 for s<0, sign(x)=+1 for x≧0.

[0055] In another embodiment, the phase of light transmitted by thecoding mask substantially follows a non-separable function of the form:

[0056] phase(r,θ) =Σ[r^(a) ^(_(i)) cos(b_(i)θ++100 _(i))]

[0057] where the sum is again over the index i.

[0058] In another embodiment the phase of light transmitted by thecoding mask substantially follows a function of the form:

[0059] Phase profile (x,y)=

[0060] 7[sign(x) |x|³+sign(y)|y|³]+7[sign(x)|x|^(9.6)+sign(y)|Y|^(9.6)]

[0061] where |x|≦1, |y|≦1.

[0062] The coding mask further may be integrally formed with a lenselement for focussing the light, or with the illumination optics.

[0063] The coding mask could comprise an optical material having varyingthickness, an optical material having varying index of refraction,spatial light modulators, or micro-mechanical mirrors.

[0064] A method for increasing depth of field and controlling focusrelated aberrations in a conventional Interference Contrast Imagingsystem comprises the steps of modifying the wavefront of transmittedlight between the Phase Object and the detector, the wavefrontmodification step selected to alter the optical transfer function of theInterference Contrast Imaging system in such a way that the alteredoptical transfer function is substantially insensitive to the distancebetween the Phase Object and the objective optics over a greater rangeof object distances than was provided by the unaltered optical transferfunction, and post processing the image captured by the detector byreversing the alteration of the optical transfer function accomplishedby the mask.

[0065] A Wavefront Coding optical element can also be used on theillumination side of the system in order to extend the depth of field ofthe projected illumination due to the duality of projection and imaging.This projected illumination would be broader than without WavefrontCoding, but the optical density as a function of distance from theobject would be less sensitive with Wavefront Coding than without.Without Wavefront Coding on the illumination side of the system, theobject can technically be imaged clearly but is not illuminatedsufficiently. See “Principal of Equivalence between Scanning andConventional Optical Imaging Systems”, Dorian Kermisch, J. Opt. Soc.Am., Vol. 67, no. 10, pp. 1357-1360 (1977).

BRIEF DESCRIPTION OF THE DRAWINGS

[0066]FIG. 1 (prior art) shows a standard prior art InterferenceContrast imaging system.

[0067]FIG. 2 (prior art) shows ray paths and polarization states for theInterference Contrast imaging system of FIG. 1.

[0068]FIG. 3 shows a Wavefront Coding Interference Contrast imagingsystem including Wavefront Coding optics and post processing inaccordance with the present invention.

[0069]FIG. 4 describes in detail the Object Modifying Function andObject Imaging Function of the Wavefront Coding Interference Contrastsystem.

[0070]FIG. 5 shows the aperture transmittance function and thecorresponding ambiguity function for the Object Imaging Function of theprior art system of FIG. 1.

[0071]FIG. 6 shows the Wavefront Coded cubic phase function and thecorresponding ambiguity function for the Object Imaging Function of FIG.3.

[0072]FIG. 7 shows another Wavefront Coded phase function and thecorresponding ambiguity function for the Object Imaging Function of FIG.3.

[0073]FIG. 8 shows misfocus MTFs for the prior art Object ImagingFunction of FIG. 1 and the Object Imaging Functions for the WavefrontCoded Interference Contrast systems described in FIGS. 3, 6 and 7.

[0074]FIG. 9 shows single plane of focus images of human cervical cellswith darkly stained nuclei imaged with a 40 ×X, NA=1.3 objective with aconventional Interference Contrast system and with a Wavefront CodedInterference Contrast imaging system similar to that of FIG. 3.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0075] Wavefront Coding can be used with conventional objectives,polarizers and beam splitters in Interference Contrast systems, as shownin FIG. 3, to achieve an increased depth of field in an optical anddigital imaging system. This can be explained by considering the ObjectModifying Functions of conventional Interference Contrast systemsseparately from the Object Imaging Functions, as shown in FIG. 4. Byconsidering these two functions separately, modification of depth offield can be explained in terms of the Object Imaging Function.Extending the depth of field of the Object Imaging Functions ofInterference Contrast systems is shown in FIGS. 5-8. FIG. 9 showsreal-world images of human cervical cells taken with a system havingonly Interference Contrast and a comparison to an image from a WavefrontCoding Interference Contrast system.

[0076]FIG. 3 shows a Wavefront Coded Interference Contrast imagingsystem 300 including Wavefront Coding and post processing in accordancewith the present invention. Similar reference numbers are used in FIG. 3as are used in FIG. 1, since the systems are very similar, except forthe addition of Wavefront Coding element 324 and post processing 326.The general Interference Contrast imaging system of FIG. 1 is modifiedwith a special purpose generalized aspheric optical element 324 andimage processing 326 of the detected image to form the final image.Unlike the conventional Interference Contrast system, the final image incombined system 300 is not directly available at detector 322. In fact,no sharp and clear image of any kind is available in system 300, exceptafter image processing 326. Image processing 326 of the detected imageis required to remove the spatial Wavefront Coding effects (other thanthe extended depth of field).

[0077] Wavefront Coding optical element 324 can be fabricated as aseparate component as shown in FIG. 3, or can be combined with objectivelens 312, tube lens 318, beam splitter 314, analyzer 316, or anycombination of these. Any material or configuration that can impart arange of spatial phase shifts to a wavefront can be used to constructWavefront Coding element 324. For example, optical glass or plastic ofvarying thickness and/or index of refraction can be used. Holograms andmirrors can also be used as the material for the Wavefront Codingelement. In order to dynamically adjust the amount of depth of field, orto essentially change the Wavefront Coding element 324 for differentobjectives or desired depth of field, spatial light modulators ordynamically adjustable micro mirrors or similar can also be used.

[0078] Wavefront Coding optical element 324 can also be used on theillumination side of system 300 in order to extend the depth of field ofthe projected illumination due to the duality of projection and imaging.This projected illumination would be broader than without WavefrontCoding, but the optical density as a function of distance from theobject would be less sensitive with Wavefront Coding than without.

[0079] The components that distinguish the Wavefront Coding InterferenceContrast system of FIG. 3 from a general or brighffield imaging systemis polarizer 304, beam splitter 306, beam splitter 314, analyzer 316,and Wavefront Coding element 324 and image processing 326. Thepolarizer, analyzer, and beam splitters essentially use phase to modifythe imaging characteristics of the object 310. The Wavefront Codingelement 324 and image processing 326 are used to increase the depth offield or remove misfocus effects in images of the modified object asshown below. By grouping the components of system 300 by their function,the Wavefront Coding Interference Contrast imaging system can beunderstood.

[0080] The locations of polarizer, analyzer, and beam splitters of FIG.3 have been chosen because of historical reasons. These are thetraditional locations for these components in prior art systems relativeto the illumination and imaging optics. The same relative locations areseen in FIG. 1. The beam splitter 314 and analyzer 316 can theoreticallybe moved relative to objective lens 312 without changing the imagingbehavior of the system. See system 400A of FIG. 4. Numbering conventionsof FIG. 4 are also similar to those of FIGS. 1 and 3 due to the similarnature of the components. In system 400A the beam splitter and analyzerhave been moved before the objective lens but after the object. Thewavefront after analyzer 416 is polarized as is the wavefront afteranalyzers 216 and 316 in FIGS. 2 and 3 respectively. Since, ideally,lenses do not change the polarization, shear, or bias of the wavefrontthis new location is technically equivalent to that of FIG. 3. Considerthe ray paths of FIG. 2. Notice that the ray paths between beamsplitters 206 and 214 are parallel. Moving beam splitter 206 beforeobjective lens 212 theoretically will not change the parallel nature ofthe ray paths. Analyzer 216 can also move before objective lens 212 withno adverse affects. The component arrangement of system 400A allows the“Object Modifying Functions” to be clearly distinguished from the ObjectImaging Functions.

[0081] In order to further characterize the Object Modifying Function ofsystem 400A consider system 400B of FIG. 4. In this system a new phaseand amplitude object 410B replaces the original object 410A of system400A. This new object is selected so that its three dimensionalstructure produces an identical wavefront from illumination source 402,polarizer 404, and illumination optics 408 as from object 410A whencombined with the polarizer, analyzer, and beam splitters of system400A. It is well known that a phase and amplitude object can betheoretically constructed so that any given linearly polarized wavefrontcan be reproduced from linearly polarized illumination. Although it istheoretically possible to produce such a new object 410B, in practice itmight be difficult. Since a new object 410B can be substituted for thecombination of original object 410A, beam splitter 406, beam splitter414, and analyzer 416, it is clear that the polarizers and analyzers actto modify the imaging characteristics of the object. Notice that theright sides of systems 400A and 400B are identical. The right sides ofthese systems are the Object Imaging Function. The Object ImagingFunction images the object that has had its imaging characteristicsmodified by the Object Modifying Function. With the Wavefront Codingoptical element 424 and image processing 426 the Object Imaging Functioncan have a very large depth of field and be able to controlfocus-related aberrations.

[0082] If the Object Imaging Function of system 400B has a large depthof field, then the New Object of 410B can be imaged over a large depth.Likewise, when the Object Imaging Function of system 400A has a largedepth of field, object 410A (as modified by the Object ModifyingFunction) can be imaged with a large depth of field. Since system 400Bproduces identical images to system 400A, and system 400A producesidentical images to system 300, this also means that system 300 willimage object 310 with a large depth of field. This large depth of fieldis also independent of the object or Object Modifying Functions as shownin FIG. 4.

[0083] The Object Imaging Function can be made to have a large depth offield by use of a generalized aspheric optical element and signalprocessing of the detected images. Ambiguity function representationscan be used to succinctly describe this large depth of field. Only themagnitude of the ambiguity functions in this and following figures areshown. Ambiguity functions are, in general, complex functions.One-dimensional systems are given for simplicity. Those skilled in theart of linear systems and ambiguity function analysis can quickly makeextensions to two-dimensional systems. An ambiguity functionrepresentation of the optical system is a powerful tool that allowsmodulation transfer functions (“MTFs”) to be inspected for all values ofmisfocus at the same time. Essentially, the ambiguity functionrepresentation of a given optical system is similar to a polar plot ofthe MTF as a function of misfocus. The in-focus MTF is described by thetrace along the horizontal v=0 axis of the ambiguity function. An MTFwith normalized misfocus value of${\psi = {\left( \frac{2\quad \pi}{\lambda} \right)W_{20}}},$

[0084] where W₂₀ is the traditional misfocus aberration coefficient andλ is the illumination center wavelength, is described in the ambiguityfunction along the radial line with slope equal to (ψ/pi). For moreinformation on ambiguity function properties and their use in WavefrontCoding see “Extended Depth of Field Through Wavefront Coding”, E. R.Dowski and W. T. Cathey, Applied Optics, vol. 34, no 11, pp. 1859-1866,April, 1995, and references contained therein.

[0085]FIG. 5 gives an ambiguity function perspective on the ObjectImaging Function of conventional Interference Contrast systems. The topplot of FIG. 5 shows the aperture transmittance function of an idealconventional Interference Contrast system such as that shown in FIG. 1.The bottom plot of FIG. 5 shows the associated ambiguity functionassociated with the Object Imaging Function for the prior art system ofFIG. 1.

[0086] Over the normalized aperture (in normalized coordinates extendingfrom −1 to +1) the conventional system has a transmittance of 1, i.e.,100%. The phase variation (not shown) is equal to zero over this range.The corresponding ambiguity function has concentrations of optical power(shown as dark shades) very close to the horizontal v=0 axis. From therelationship between the ambiguity function and misfocused MTFs, we seethat the conventional Interference Contrast Systems has a small depth offield because slight changes in misfocus lead to MTFs (represented byradial lines with non-zero slope in the ambiguity function) thatintersect regions of small power.

[0087]FIG. 6 shows an example of a phase function for the WavefrontCoding optical element 324 and corresponding ambiguity function for animproved system of FIG. 3. This phase function is rectangularlyseparable and can be mathematically described in two dimensions as:

[0088] Phase (x,y)=12[x³+y³]

[0089] |x|≦1, |y|≦1.

[0090] Only one dimension of this phase function is shown in the upperplot of FIG. 6. Increasing the peak-to-valley phase height (as can bedone by increasing the constant 12 above), results in increasing depthof field. The transmittance of this system (not shown) is unity (i.e.,100%) over the entire aperture, as in the top plot of FIG. 5.

[0091] The ambiguity function shown in FIG. 6 for this Wavefront CodedInterference Contrast system is seen to have optical power spread over amuch larger region in the ambiguity domain than does thediffraction-limited system plotted in FIG. 5. Broader regions of opticalpower in the ambiguity function translate to larger depth of field ordepth of focus since the ambiguity function is essentially a radial plotof misfocused MTFs with the angular dimension pertaining to misfocus.Thus, this Wavefront Coded Interference Contrast system has a largerdepth of field than the conventional Interference Contrast system.

[0092] There are an infinite number of different Wavefront Coding phasefunctions that can be used to extend the depth of field. Other moregeneral rectangularly separable forms of the Wavefront Coding phasefunction are given by:

[0093] phase(x,y)=Σ[a_(i) sign(x)|x|^(b) ^(_(i)) +c_(i sign(y)|Y|) ^(d)^(_(i)) ]

[0094] where the sum is over the index i,

[0095] sign(x)=−1 for x<0, sign(x)=+1 for x≧0.

[0096] Rectangularly separable forms of Wavefront Coding allow fastprocessing. Other forms of Wavefront Coding complex phases arenon-separable, and the sum of rectangularly separable forms. Onenon-separable form is defined as:

[0097] phase(r,θ) =E[r ^(a) ^(_(i)) cos(b_(i θ+φ) _(i))

[0098] where the sum is again over the index i.

[0099]FIG. 7 shows the Wavefront Coding phase function and the ambiguityfunction for a further improved system of FIG. 3. The top plot of FIG. 7shows the phase function from FIG. 6 (curve 701) and a further improvedphase function (curve 702). The aperture transmittance function is thesame as shown in FIG. 5. The form of the new phase profile 702, inradians, of this system is given by:

[0100] Phase profile (x,y)=

[0101]7[sign(x)|x| ³+sign(y)|y|³]+7[sign(x)|x|^(9.6)+sign(y)|y|^(9.6)]

[0102] where |x|≦1, |y|≦1.

[0103] The ambiguity function related to phase function 702 is shown inthe bottom of FIG. 7. This ambiguity function is seen to have moreoptical power uniformly spread about the horizontal v=0 axis whencompared to either the Wavefront Coding Interference Contrast systemplotted in FIG. 6 or the Conventional Interference Contrast systemplotted in FIG. 5. Thus, the Wavefront Coded Interference Contrastsystem of FIG. 7 will have a larger depth of field than the systemsrepresented in FIGS. 6 or 5.

[0104]FIG. 8 shows MTFs as a function of misfocus for the prior artInterference Contrast system, and the Wavefront Coded InterferenceContrast systems of FIGS. 6 and 7. The top plot of FIG. 8 shows the MTFsof the conventional Interference Contrast imaging system of FIG. 1 andFIG. 5 and the MTFs of the Wavefront Coded Interference Contrast systemof FIG. 6. The bottom plot shows the MTFs of the Interference Contrastimaging system of FIGS. 1 and 5 (again) and the MTFs from the WavefrontCoding Interference Contrast imaging system of FIG. 7. These plots arethe particular MTFs given in the respective ambiguity functions for thenormalized misfocus values ψ={0, 2, 4}. Notice that the MTFs for theconventional Interference Contrast system (top and bottom plots) varyappreciably with even this slight amount of misfocus. The image from theconventional system will thus change drastically due to misfocus effectsfor only small, misfocus values. This is expected from the narrowambiguity function associated with the conventional system (shown inFIG. 5).

[0105] By comparison, the MTFs from the Wavefront Coded InterferenceContrast imaging systems (top and bottom plots) show very little changewith misfocus as predicted by the ambiguity functions associated withthese systems (shown in FIGS. 6 and 7). If the MTFs of the system do notchange, the resulting MTFs (and hence also point spread functions, or“PSFs”) can be corrected over a large range of misfocus with a singlepost processing step 326. A single post processing step is not possiblewith conventional systems, which change appreciably with misfocus sincethe MTFs and PSFs of the system change with misfocus to values that areunknown and often impossible in practice to calculate. The MTFs from theWavefront Coded Interference Contrast system in the top plot are seen tohave lower values for most spatial frequencies than the MTFs from theWavefront Coded Interference Contrast system of the bottom plot. This isexpected from the ambiguity functions of FIGS. 6 and 7 respectively. Thetwo-term phase function (curve 702) yields MTFs that not only havesimilarly small change with misfocus but also give a higher MTF thanthose associated with the simple cubic phase function (curve 701). Thishigher MTF results in a more compact PSF (not shown) as well as lesssignal-to-noise ratio penalties needed for the image processing 326.

[0106] In general, the Wavefront Coded objective mask phase functionthat yields the smallest MTF variation with misfocus and also thehighest MTF is preferred in practice. There are an infinite number ofdifferent objective mask phase functions that are good candidates forcontrol of the MTF. The characteristics that practical Wavefront Codingmask phase functions have can generally be described as being relativelyflat near the center of the aperture with increasing and decreasingphase near the respective edges of the aperture. The central portion ofthe phase function controls the majority of the light rays that wouldnot need modification if the objective were stopped down, for the depthof field extension required. For increasing amounts of depth of field,the size of the central phase region that can be flat decreases.Increasing the flatness of the central region of the rays leads tolarger MTFs as seen in comparison to the phase functions and MTFs ofFIGS. 6, 7, and 8. The edge portion of the phase function controls thelight rays that increase the light gathering and spatial resolution ofthe full aperture system but, without modification, cause the largestamount of misfocus effects in traditional systems. It is these edge raysthat should be modified most by the objective mask phase functionbecause they control the variation of the MTFs and PSFs with misfocus.The actual modification made to these edge rays should position them sothat the sampled PSFs and MTFs are maximally insensitive to changes inmisfocus.

[0107] Notice that the MTFs from the Wavefront Coding InterferenceContrast system of FIG. 8 (upper and lower plots) essentially do notchange with misfocus but also do not have the same shape as that of thein-focus MTF (ψ=0) of the conventional Interference Contrast system. Inthe spatial domain, the Wavefront Coding Interference Contrast systemsform images with a specialized blur where the blur is insensitive to theamount of misfocus. The Image Processing function 326 is used to removethis blur. The Image Processing function can be designed so that afterprocessing the MTFs and PSFs of the combined Wavefront CodingInterference Contrast system, over a range of misfocus, closely matchthat of the in-focus Interference Contrast system. The Image Processingfunction can also produce an effective MTF that has more or lesscontrast than the in-focus Interference Contrast system, depending onthe needs of the particular application.

[0108] In essence, the image processing function restores the WavefrontCoding Interference Contrast transfer functions to those expected fromthe conventional Interference Contrast system with no misfocus. Sinceall the Wavefront Coding MTFs are essentially identical, after imageprocessing 326 all MTFs (and hence all PSFs) will be nearly identicalfor each value of misfocus.

[0109] More specifically, the image processing function, say F,implements a transformation on the blurred Wavefront Coding InterferenceContrast system, say H_(WFC), so that after processing the system has anideal response H_(ideal). Typically the ideal response is chosen as thein-focus response from the general Interference Contrast system. Ifimplemented as a linear filter, then F is (in the spatial frequencydomain) equivalent to:

[0110] F(w) H_(WFC)(W) =H_(ideal)(W)

[0111] where w denotes a spatial frequency variable. If the idealresponse is fixed then changing the Wavefront Coding InterferenceContrast system H_(WFC) changes the image processing function F. The useof a different Wavefront Coding phase function can cause a change in theimage processing function. In practice, it is common to be able tomeasure slight changes in the Wavefront Coding Interference Contrastsystem as a function of misfocus. In this case the image processing F ischosen as a best fit between the measured data and the desired systemafter processing.

[0112] There are many linear and non-linear prior art techniques forremoving known and unknown blur in images. Computationally effectivetechniques include rectangularly separable or multi-rank linearfiltering. Rectangularly separable linear filtering involves a two stepprocess where the set of one-dimensional columns are filtered with aone-dimensional column filter and an intermediate image is formed.Filtering the set of one-dimensional rows of this intermediate imagewith a one-dimensional row filter produces the final image. Multi-rankfiltering is essentially the parallel combination of more than onerectangularly separable filtering operation. A rank N digital filterkernel can be implemented with rectangularly separable filtering byusing N rectangularly separable filters in parallel.

[0113] The form of the processing (rectangularly separable, multi-rank,2D kernel, etc.) is matched to that of the Wavefront Coding element.Rectangularly separable filtering requires a rectangularly separableWavefront Coding element. The element described in FIG. 6 isrectangularly separable.

[0114]FIG. 9 contains real world images of human cervical cells madewith a conventional Interference Contrast system and a Wavefront CodedInterference Contrast System. The image on the left of FIG. 9 was madewith a conventional 40×, NA=1.3 Interference Contrast system similar tothat of FIG. 1. The image on the right of FIG. 9 was made with aWavefront Coding Interference Contrast system similar to that of FIG. 3.The Wavefront Coding Element 324 was a rectangularly separable cubicphase element. Rectangularly separable digital filtering was used forimage processing 326.

[0115] Notice the phase shading visible in the conventional image. Thisphase shading results in a 3D-like appearance of the object. This is acharacteristic of Interference Contrast imaging. Notice also that manyparts of the Interference Contrast images are blurred due to misfocuseffects. The bottom part of the left image, for example, is particularlybadly blurred by misfocus. The Wavefront Coded Interference Contrastimage is also seen to have similar phase shading and 3D-like appearanceas the conventional image. The depth of field visible in the image ismuch larger in the Wavefront Coded image than in the conventional image.Many parts of the cells that could not be resolved in the conventionalimage are clearly visible in the Wavefront Coding image. Thus, theWavefront Coding Interference Contrast image produces both thecharacteristic Interference Contrast phase object imagingcharacteristics and a large depth of field.

[0116] As shown in FIGS. 6 through 9, the Wavefront Coding InterferenceContrast imaging system removes the effects of misfocus on the finalimages. The Wavefront Coding Interference Contrast system will controlthe misfocus effects independent of the source of the misfocus. Whenincreasing the depth of field, as shown in FIG. 9, the misfocus effectsare produced from the object or parts of the object not being in thebest focus position relative to the imaging optics. Misfocus effects canalso be produced by non-ideal optics, temperature changes, mechanicalpositioning errors, and similar causes that lead to optical aberrations.Controlling misfocus effects besides those related to object positioningallows inexpensive systems to be produced that image with a highquality. For example, if the objective lens 312 of FIG. 3 has anoticeable amount of chromatic aberration then misfocus effects will beproduced as a function of illumination wavelength. The Wavefront CodingInterference Contrast system can control the chromatic abberationmisfocus effects while also extending the depth of field. Other opticalaberrations that can similarly be controlled include petzval curvature,asigmatism, spherical aberration, temperature related misfocus, andfabrication or alignment related misfocus. Many other aberrations inprior art systems may be improved in Wavefront Coding InterferenceContrast systems

What is claimed is:
 1. Apparatus for increasing depth of field andcontrolling focus related aberrations in an Interference ContrastImaging system having an illumination source, optical elements fordividing light polarizations, and illumination optics placed before aPhase Object to be imaged, and elements for recombining lightpolarizations and objective optics after the Phase Object to form animage at a detector, the improvement comprising: an optical WavefrontCoding mask having an aperture and placed between the Phase Object andthe detector, said coding mask being constructed and arranged to alterthe optical transfer function of the Interference Contrast Imagingsystem in such a way that the altered optical transfer function issubstantially insensitive to the distance between the Phase Object andthe objective optics over a greater range of object distances than wasprovided by the unaltered optical transfer function, wherein the codingmask affects the alteration to the optical transfer functionsubstantially by affecting the phase of light transmitted by the mask;and a post processing element for processing the image captured by thedetector by reversing the alteration of the optical transfer functionaccomplished by the coding mask.
 2. The apparatus of claim 1 wherein thedetector is a charge coupled device (CCD).
 3. The apparatus of claim 1,wherein the phase of light transmitted by the coding mask is relativelyflat near the center of the aperture with increasing and decreasingphase near respective ends of the aperture.
 4. The apparatus of claim 1,wherein the phase of light transmitted by the coding mask substantiallyfollows a cubic function.
 5. The apparatus of claim 4, wherein the phaseof light transmitted by the coding mask substantially follows a functionof the form: Phase (x,y)=12[x³+y³] |x|≦1, |y|≦1.
 6. The apparatus ofclaim 1, wherein the phase of light transmitted by the coding masksubstantially follows a rectangularly separable sum of powers functionof the form: phase(x,y)=Σ[a_(i) sign(x)|x|^(b) ^(_(i)) +c_(i)sign(y)|y|^(d) ^(_(i)) ] where the sum is over the index i, sign(x)=−1for x<0, sign(x)=+1 for x≧0.
 7. The apparatus of claim 1, wherein thephase of light transmitted by the coding mask substantially follows anonseparable function of the form: phase(r,θ)=Σ[r ^(a) ^(_(i))cos(b_(i)θ+φ_(i)) ]where the sum is again over the index i.
 8. Theapparatus of claim 1, wherein the phase of light transmitted by thecoding mask substantially follows a function of the form: Phase profile(x,y)=7[sign(x)|x|³+sign(y)|Y|³]+7[sign(x)|x|^(9.6)+sign(y)|j|^(9.6)]where|x|≦1, |y|≦1.
 9. The apparatus of claim 1, wherein the coding maskfurther comprises a lens element for focussing the light.
 10. Theapparatus of claim 1, wherein the coding mask is integrally formed withthe illumination optics.
 11. The apparatus of claim 1, wherein thecoding mask comprises an optical material having varying thickness. 12.The apparatus of claim 1, wherein the coding mask comprises an opticalmaterial having varying index of refraction.
 13. The apparatus of claim1, wherein the coding mask comprises spatial light modulators.
 14. Theapparatus of claim 1, wherein the coding mask comprises micro-mechanicalmirrors.
 15. A method for increasing depth of field and controllingfocus related aberrations in a conventional Interference ContrastImaging system having an illumination source, optical elements fordividing light polarizations, and illumination optics placed before aPhase Object to be imaged, and elements for recombining lightpolarizations and objective optics after the Phase Object to form animage at a detector, the method comprising the steps of: between thePhase Object and the detector, modifying the wavefront of transmittedlight with a wavefront coding mask; the wavefront modification stepselected to alter the optical transfer function of the InterferenceContrast Imaging system in such a way that the altered optical transferfunction is substantially insensitive to the distance between the PhaseObject and the objective optics over a greater range of object distancesthan was provided by the unaltered optical transfer function; and postprocessing the image captured by the detector by reversing thealteration of the optical transfer function accomplished by the mask.16. The method of claim 15, wherein the modifying step modifies thephase of light transmitted according to a profile which is relativelyflat near the center of the aperture with increasing and decreasingphase near respective ends of the aperture.
 17. The method of claim 15,wherein the phase of light transmitted by the mask substantially followsa cubic function. wherein the phase of light transmitted by the codingmask substantially follows a function of the form: Phase(x,y)=12[x^(3 +y) ^(3 ] where |x|≦)1, |y|≦1.
 18. The method of claim 15,wherein the phase of light transmitted by the coding mask substantiallyfollows a rectangularly separable sum of powers function of the form:phase(x,y)=Σ[a_(i) sign(x)|x|^(b) ^(_(i)) +c_(i)sign(y)|Y|^(d) ^(_(i))]where the sum is over the index i, sign(x)=−1 for x<0, sign(x)=+1 forx≧0.
 19. The apparatus of claim 15, wherein the phase of lighttransmitted by the coding mask substantially follows a non-separablefunction of the form: phase(r,θ)=Σ[r^(a) ^(_(i)) cos(b_(i)0+φ_(i))]where the sum is again over the index i.
 20. The method of claim 15,wherein the phase of light transmitted by the coding mask substantiallyfollows a function of the form: Phase profile(x,y)=7[sign(x)|x|³+sign(y)|y|³]+7[sign(x)|x|^(9.6)+sign(y)|Y|^(9.6)]where |x|≦1, |y|≦1.
 21. A Wavefront Coding Interference Contrast Imagingsystem for imaging a Phase Object comprising: an illumination source forproviding illumination; polarizing optics for splitting the illuminationinto distinct juxtaposed polarizations; illumination optics placedbetween the illumination source and the Phase Object; polarizing opticsfor recombining the illumination polarizations; a detector; objectiveoptics placed between the Phase Object and the detector to form an imageat the detector; an optical Wavefront Coding mask having an aperture andplaced between the Phase Object and the detector, said mask beingconstructed and arranged to alter the optical transfer function of theImaging system in such a way that the altered optical transfer functionis substantially insensitive to the distance between the Phase Objectand the objective optics over a greater range of object distances thanwas provided by the unaltered Imaging system optical transfer function,wherein the mask affects the alteration to the optical transfer functionsubstantially by affecting the phase of light transmitted by the mask;and a post processing element for processing the image captured by thedetector by reversing the alteration of the optical transfer functionaccomplished by the mask.
 22. The apparatus of claim 21, wherein thephase function of light transmitted by the coding mask is relativelyflat near the center of the aperture with increasing and decreasingphase near respective ends of the aperture.
 23. In an imaging system ofthe type having partially coherent radiation between an object and animage of the object, the improvement comprising: a wavefront codingoptical element for modifying a phase function of the partially coherentradiation to increase a depth of field of the image; and a postprocessing element for processing the image to modify effects induced bythe wavefront coding element in the image so as to generate a finalimage of the object.
 24. In the imaging system of claim 23, the imagingsystem comprising a contrast imaging system.
 25. In the imaging systemof claim 23, the wavefront coding element being one or a combination of(a) one or more separate optical elements within the imaging system, (b)one or more optical modifications to one or more optical elementsurfaces of the imaging system.
 26. In the imaging system of claim 25,one or both of the separate optical elements and modificationscomprising one or both of holograms and mirrors.
 27. In the imagingsystem of claim 23, the wavefront coding element comprising opticalmaterial with varying optical thickness.
 28. In the imaging system ofclaim 23, the wavefront coding element being one or a combination of (a)one or more separate optical elements within the imaging system, (b) amodification to one or more surfaces of optical elements of the imagingsystem.
 29. In the imaging system of claim 23, the wavefront codingelement comprising optical material with varying index of refraction.30. In the imaging system of claim 23, further comprising a detector atthe image, the post processing element connected with the detector toprocess electronic images of the detector.
 31. In the imaging system ofclaim 23, the object comprising a phase object.
 32. An interferencecontrast imaging system, comprising: an illumination source; a polarizerfor generating polarized light from the illumination source;illumination optics for focusing the polarized light onto a phaseobject; a detector; an objective lens, tube lens and wavefront codingelement for forming an image of the phase object on the detector, thewavefront coding element modifying phase of a wavefront generating theimage; a post processor connected with the detector for post processingimages from the detector to generate a final image by reversing phaseeffects induced by the wavefront coding element.